Related rates(calculus)the radius of a sphere is increasing at a rate of  4  mm/s. how fast is the volume increasing when the diameter is  100  mm?

The volume increases at a rate of

Step-by-step explanation:

The rate of change of the radius with respect to time is 4 mm / s.

So:

Now we must find a relationship between the volume of a sphere and its radius.

The equation of the volume of a sphere is:

So:

The diameter of the sphere is 100 mm. Therefore its radius is 100/2 = 50 mm.

So:

The volume increases at a rate of :

40000 π mm ^ 3 / s = 125663.71 mm^3/s